Download Deciding to Enter a Monetary Union

WP/12/240
Deciding to Enter a Monetary Union: The
Role of Trade and Financial Linkages
Ruy Lama and Pau Rabanal
© 2012 International Monetary Fund
WP/12/240
IMF Working Paper
Institute for Capacity Development
Deciding to Enter a Monetary Union: The Role of Trade and Financial Linkages
Prepared by Ruy Lama and Pau Rabanal1
Authorized for distribution by Jorge Roldós
October 2012
This Working Paper should not be reported as representing the views of the IMF.
The views expressed in this Working Paper are those of the author(s) and do not necessarily represent
those of the IMF or IMF policy. Working Papers describe research in progress by the author(s) and are
published to elicit comments and to further debate.
Abstract
This paper evaluates the role of trade and financial linkages in the decision to enter a monetary
union. We estimate a two-country DSGE model for the U.K. economy and the euro area, and use
the model to compute the welfare trade-offs from joining the euro. We evaluate two alternative
scenarios. In the first one, we consider a reduction of trade costs that occurs after the adoption of a
common currency. In the second, we introduce interest rate spread shocks of the same magnitude
as the ones observed during the recent debt crisis in Europe. The reduction of trade costs generates
a net welfare gain of 0.9 percent of life-time consumption, while the increased interest rate spread
volatility generates a net welfare cost of 2.9 percentage points. The welfare calculation suggests
two ways to preserve the welfare gains in a monetary union: ensuring fiscal and financial stability
that reduces macroeconomic country risk, and increasing wage flexibility such that the economy
adjusts to external shocks faster.
JEL Classification Numbers: E52; F41; F42; F44.
Keywords: Trade Costs; DSGE Model; Monetary Union.
Author’s E-Mail Address
1
[email protected]; [email protected]
Mr. Lama is an Economist in the European Department and Mr. Rabanal is an Economist in the Western
Hemisphere Division of the IMF Institute. We thank Jorge Roldós, Gaston Gelos, Mick Devereux and seminar
participants at the IMF Institute, the Federal Reserve Board, and the 2011 Society of Computational Economics
Conference for their useful comments. All errors are our own.
Contents
Page
1. Introduction ...........................................................................................................................3
2. The Model ..............................................................................................................................7
2.1 Households, International Assets Markets, and Staggered Wage Setting ...............8
2.2 Firms ......................................................................................................................10
2.3 Closing the Model ..................................................................................................12
3. Bayesian Estimation.............................................................................................................13
3.1 Data ........................................................................................................................13
3.2 Model Dynamics and Data Transformations .........................................................14
3.3 Estimation: Priors and Posteriors ..........................................................................15
4. Policy Analysis: Welfare Gains of Entering a Monetary Union..........................................21
5. Sensitivity Analysis .............................................................................................................27
6. Conclusions ..........................................................................................................................29
Technical Appendix .................................................................................................................32
References ................................................................................................................................43
Tables
Table 1
Table 2
Table 3
Table 4
Table 5
Table 6
Table 7
Figures
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Calibrated Parameters .........................................................................................16
Prior Distributions...............................................................................................17
Posterior Distributions, structural parameters ....................................................19
Posterior Distributions, shocks parameters .........................................................19
Second Moments.................................................................................................21
Steady State Effects and Welfare Gains .............................................................24
Business Cycle Effects and Welfare Gains.........................................................26
Monetary Policy Rates in United Kingdom and the Euro Area: 1999-2011 .....47
Trade with Euro Area in France, Germany, Italy, Spain and the United
Kingdom ...........................................................................................................48
Risk Premium in France, Italy, Spain the United Kingdom ..............................49
Impulse Response Functions to 25 basis points increase in UIP Shock............50
Sensitivity Analysis of Welfare .........................................................................51
2
1
Introduction
The economic crisis that started in 2007 has revived the debate on the bene…ts
and costs of belonging to the European Monetary Union (EMU). The recent
crisis has been particularly long lasting in some southern European countries,
leaving a large public and private debt overhang. This situation is making it
di¢ cult to provide additional …scal stimulus and is forcing deleveraging in the
banking sector. In addition, exchange rate policy cannot be used as a tool to
correct competitiveness problems and increase growth through net exports.
As a result, some economists and market commentators have suggested that
the costs of belonging to the EMU, also known as the euro area, might
outweigh its bene…ts for some of its members.1 The costs of belonging to the
EMU are mostly related to the loss of monetary and exchange rate policy
as an instrument for macroeconomic stabilization. These costs are ampli…ed
by the EMU’s design ‡aws, most notably the lack of …scal and labor market
integration that are needed in an optimal currency area (Mundell, 1961).
However, all the costs of a monetary union have to be assessed relative to
the bene…ts brought about by lower transaction costs associated to having a
common currency, and the disappearance of nominal exchange rate risk.
While this debate is taking place, the EMU has actually expanded since
the beginning of the crisis: Malta and Cyprus joined in 2008, Slovakia in
2009, and Estonia in 2011. In fact, all country members of the European
Union (EU) are expected to participate in the EMU once the convergence
criteria are ful…lled. Yet, some countries have made it clear that they are not
interested in joining the EMU. The United Kingdom (U.K.) and Denmark
were granted opt-out clauses in 1997 and 1993 respectively. Both countries
consider that the decision of entering the EMU should be approved by a
referendum. Sweden never ful…lled the conditions to adopt the euro, by not
entering the European Exchange Rate Mechanism (ERM II), which requires
keeping the country’s exchange rate in a narrow band with the euro for two
years.
In the case of the U.K., the government of prime minister Tony Blair
set in 1997 …ve economic tests to evaluate whether or not the country will
bene…t from adopting the euro.2 The …ve economic tests are :
1. Are business cycles and economic structures compatible so that we
1
2
See Feldstein (2010) and Roubini (2011).
See HM Treasury (1997).
3
and others could live comfortably with the euro interest rates on a
permanent basis?
2. If problems emerge is there su¢ cient ‡exibility to deal with them?
3. Would joining EMU create better conditions for …rms making long-term
decisions to invest in Britain?
4. What impact would entry into EMU have on the competitive position of
the U.K.’s …nancial services industry, particularly the City’s wholesale
markets?
5. In summary, will joining EMU promote higher growth, stability and a
lasting increase in jobs?
The British government conducted two evaluations: one in 1997 and the
other in 2003. The 1997 report determined that the U.K. did not satisfy
the …ve economic tests. The 2003 report mentioned that even though EMU
membership could increase U.K. GDP between 5 and 9 percent, there was
not a clear and unambiguous case for adopting the euro.3 The British current administration has pledged not to join the EMU over the course of the
Parliament.4
Figure 1 illustrates the potential constraints that the U.K. economy would
have faced if it had joined the EMU. Figure 1 plots the times series of the
reference monetary policy rates set by the Bank of England (BoE) and the
European Central Bank (ECB). In the recent period of …nancial turbulence
(since 2007), the di¤erence between the short-term interest has been less than
one percentage point due to the synchronized e¤ects of the Great Recession.
The two reference rates have di¤ered by more than 100 basis points quite
often. For instance, between 2001 and 2005 the interest rate di¤erential
increased from 100 to 300 basis points. These di¤erences are quite large
and can have important macroeconomic e¤ects on output and in‡ation.5
3
See HM Treasury (2003).
On October 5, 2011, Prime Minister David Cameron stated in a speech at the
annual conservative party conference the following: "So let me say this: as long
as I’m prime minister, this country will never join the euro". Speech available
at http://www.telegraph.co.uk/news/politics/david-cameron/8809209/David-Cameronsspeech-to-Conservative-Party-Conference.html.
5
For empirical evidence on the transmission mechanism of monetary shocks in the U.K.
see DiCecio and Nelson (2007).
4
4
If the British economy had followed the nominal interest rate to the level
set by the ECB, it would have been more di¢ cult to stabilize in‡ation and
output over that period.6 Moreover, Figure 1 does not show the e¤ects that
unconventional monetary policies have had in long-term rates in the U.K.
(we will comment on the e¤ects of that policy below, in Figure 3).
Besides the costs in terms of relinquishing monetary policy and increased
macroeconomic volatility, in this paper we consider two elements that are
crucial in the decision of joining a currency area. The …rst element is the
trade expansion that typically occurs after joining in a monetary union, due
to lower transaction costs and disappearance of nominal exchange rate uncertainty.7 Figure 2 shows the expansion of trade in the euro area, measured
as trade with the euro area (imports and exports) as percent of GDP. From
1990 until 2002, the share of intraregional trade of the largest economies of
the euro area (Germany, France, Italy and Spain) increased from 16 to 23
percent of GDP. On the other hand, the U.K., who belongs to the EU but
not to the EMU has experienced a more modest increase in trade with its
EMU partners. We consider this expansion of trade as part of the bene…ts
of joining a monetary union.8
The second key element of our analysis is the role of …nancial factors,
as re‡ected in country risk premia. Figure 3 plots the 10-year government
bond interest di¤erential vis-a-vis the 10-year German bund. In the years
before EMU accession, there was signi…cant reduction of spreads for France,
Italy, and Spain. Once the euro was created, this premium disappeared
for EMU members because all government bonds where perceived to be the
same by market participants. For France, Italy and Spain, this premium
was lower than the one observed for the U.K. So if one where to study the
EMU experience between 1999 and 2007, one would reach the conclusion
that the risk premia had disappeared, and this had a positive welfare impact
6
Entering the EMU may increase the synchronization of business cycles between the
new member and the monetary union, reducing the costs of losing the ability to conduct
monetary policy (Rose, 2008). However, the existing in‡ation di¤erentials across EMU
members indicate there is no full synchronization of business cycles. Rabanal (2009)
provides with a DSGE model based evaluation of in‡ation di¤erentials in the EMU.
7
See Anderson and Wincoop (2004) and Rose (2008).
8
For these countries, we also calculated the ratio of the sum of imports and exports
with the euro area, relative to the sum of total imports and exports, obtaining the same
qualitative results in terms of trade expansion. Santos Silva and Tenreyro (2010) provide
a literature review on all the costs and bene…ts discussed in the literature of optimal
currency areas.
5
in countries that are net debtors. Since the summer of 2007, this trend
reversed and country risk premia became positive again. In the case of Italy
and Spain, the di¤erential has ‡uctuated between 200 and 600 basis points
during 2010 and 2012, while the same spread has edged down for the U.K.
Bean (2011) quanti…es the e¤ects of unconventional monetary policy in the
U.K. to have helped bring long term rates down by about 100 basis points.9
In this paper, we also evaluate how changes both in the level and volatility of
the risk premium observed in the recent crisis impact the decision of adopting
the euro.
The objective of this paper is to contribute to the debate on the desirability to join the EMU, with a novel focus on interest rate spread shocks.
Our approach is to conduct this evaluation in an estimated dynamic stochastic general equilibrium (DSGE) model. The advantage of a fully-‡edged
DSGE model is that it can measure the impact of a change of policies (in this
case, to join the euro area) on households’ and …rms’ decisions, and hence
it should be Lucas-critique free. The starting point of the analysis is a twocountry version of the Smets and Wouters (2007) general equilibrium model
with nominal and real rigidities, which includes trade and …nancial linkages
across countries. In particular, we follow Rabanal and Tuesta (2010) and
incorporate incomplete …nancial markets and local currency pricing for exports. Parameter estimation is conducted with Bayesian methods and using
data for the euro area and the U.K.
Using the estimated DSGE model, we compare the gains from having
lower transaction costs in a monetary union, with the costs of increased
macroeconomic volatility due to the loss of monetary and exchange rate
policy. Then, we consider two di¤erent hypotheses regarding the behavior
of interest rate spreads after EMU membership.10 Our results show that in
tranquil times, lower trade costs in a monetary union generate a net welfare
gain of 0.9 percentage points of life-time consumption. Even though a country
loses its monetary and exchange rate policy, the expansion of trade more
than compensates for the welfare costs of higher macroeconomic volatility.
On the other hand, in a scenario of …nancial turbulence similar to what some
southern European countries have faced during the crisis, the net welfare
costs are 2.9 percent of life-time consumption. Even though in tranquil times
9
See http://www.bankofengland.co.uk/publications/Documents/speeches/2011/speech478.pdf
This exercise complements in a more formal way, the 5 economic tests proposed by
former British prime minister Tony Blair in 1997.
10
6
the welfare calculation of entering a monetary union might give a positive
result, that can be easily be reverted in times of …nancial turbulence. This
results gives a rationale to emphasize policies of …nancial stability and …scal
prudence in a monetary union. These help to reduce macroeconomic country
risk and should help stabilize the risk premium over the business cycle.
The analysis in this paper abstracts from some issues that are relevant in
the current crisis such as the role of collateral constraints at the household
or corporate levels. In addition, we do not consider the restrictions imposed
by shifting market sentiment on the ability to conduct countercyclical …scal
policy, which is needed during a severe recession in a currency union. The
high levels of public and private debt would make the U.K. vulnerable to
changes in capital ‡ows or …nancing conditions during a situation of …nancial
stress. Although we do not model these elements in this paper, we think that
they would only increase the costs of belonging to a monetary union during
times of …nancial turbulence. Hence, our main result of high net welfare costs
under …nancial shocks would be preserved if we included these additional
features.11
The paper is organized as follows. Section 2 describes the model. Section
3 discusses the Bayesian estimation and the business cycle properties of the
model. Section 4 presents the welfare analysis. A sensitivity analysis is
conducted in Section 5. Section 6 concludes.
2
The Model
This section presents the stochastic two country model that will be used to
analyze linkages between the euro area and the U.K. The model is a twocountry version of a DSGE model similar to those by Christiano, Eichenbaum
and Evans (2005) and Smets and Wouters (2003, 2007), where we include
trade and …nancial linkages across countries.12 We discuss the main functional forms and describe the most important frictions of the economy, while
in the appendix, we provide a detailed derivation of the model. We assume
that there are two countries, home and foreign, of sizes n and 1 n, respectively. Each country produces a continuum of intermediate goods, indexed by
11
For a model of a monetary union with a …nancial accelerator friction and …scal policy
constraints see Erceg and Lindé (2010).
12
Rabanal and Tuesta (2010) have estimated a similar model for the United States and
the euro area.
7
h 2 [0; n] in the home country and f 2 [n; 1] in the foreign country, which are
traded internationally. These intermediate goods are used in the production
of the …nal good that is used for domestic …nal consumption, investment, and
government spending, and hence it is not traded across borders. The model
also incorporates linear shipping costs of moving goods internationally. As it
is typically done in the literature, we follow Samuelson (1954) and introduce
"iceberg" shipping costs.13 As we discuss throughout the paper, the main
bene…t of joining the currency area is that a fraction of these costs would
disappear, leading to more trade creation.14
The model also includes several nominal and real frictions that are important to explain the data. We include habit formation in consumption,
adjustment costs to investment, staggered price setting with indexation, and
staggered wage setting. Our benchmark model assumes that there is local
currency pricing for goods that are shipped internationally. In addition, we
assume that there is an incomplete asset market structure at the international
level: agents only have access to one non-contingent bond that is denominated in foreign-country currency. The model incorporates 14 shocks because
in the econometric section we are interested in explaining 13 variables. Unless
speci…ed in the text, all shocks follow zero-mean AR(1) processes in logs.
2.1
Households, International Assets Markets, and Staggered Wage Setting
In each country, households obtain utility from consuming …nal goods (Ctj )
with external habit formation, and dislike supplying labor (Ntj ). They are
subject to intertemporal (Dc;t ) and intratemporal (Dn;t ) preference shocks:
#
"
1
j 1+
X
N
t
t
;
(1)
E0
Dc;t log Ctj bCt 1
Dn;t
1
+
t=0
where
2 [0; 1] is the discount factor, b 2 [0; 1] is the habit parameter,
and > 0 is the inverse elasticity of labor supply with respect to the real
wage. Markets are complete within each country and incomplete at the
13
For applications of international macroeconomics models with shipping costs see Obstfeld and Rogo¤ (2000), Ravn and Mazzenga (2004), and Kose and Yi (2006).
14
The reduction in "iceberg" costs captures not only the lower transaction costs associated with engaging in international trade with only one currency, but also the bene…ts of
a decrease in nominal exchange rate volatility.
8
international level. The budget constraint of home-country households is
given by:
Pt Ctj
+
Itj
Btj
+ +
Rt R
St Dtj
t
St Dt
Yt Pt
Ut
+Tt = Btj 1 +St Dtj 1 +Wtj Ntj +Pt RtK Ktj 1 +
j
j
t+ t;
(2)
where
and
denote holdings of the domestic and foreign currency denominated bonds, Rt is the home country gross nominal interest rate and Rt
is the foreign country gross nominal interest rate. St is the nominal exchange
rate expressed in units of domestic currency needed to buy one unit of foreign
currency and Pt is the price level of the …nal good. Tt are lump-sum taxes
that are used to …nance government spending. jt denotes the payo¤ from
engaging in trade of domestic state-contingent securities.15
Home-country households also face a cost of undertaking positions in the
foreign bonds market. The (:) function captures this cost and depends on
the aggregate real holdings of the foreign assets in the entire economy, and
therefore is taken as given by individual households.16 We also include an
exogenous shock (Ut ) to the function (:), which helps explains deviations
from the uncovered interest rate parity condition. For this reason, we call this
shock the "uncovered interest rate parity" (UIP) shock.17 The risk sharing
condition, which forms the basis of the real exchange rate determination
under incomplete markets, reads:
Btj
Et
Dtj
Ct b Ct 1 Dc;t+1 Pt
Ct+1 bCt Dc;t Pt+1
= Et
Ct bCt 1 Dc;t+1 St+1 Pt
Ct+1 bCt Dc;t St Pt+1
S t Dt
Yt Pt
Ut ;
(3)
where starred variables denote foreign-country counterparts to domestic variables. As is standard in international macroeconomic models, the risk sharing
condition under incomplete markets equates the expected payo¤s of investing
15
In order to keep notation simple, we do not make the structure of the complete domestic asset markets explicit.
16
This cost induces stationarity in the net foreign asset position. See Schmitt-Grohé
and Uribe (2003) for applications in small open economy models, and Benigno (2009) in
two-country models.
17
Since the model does not include risk, we choose to not label this shock as a “risk
premium” shock. However, in the welfare evaulation exercises, we calibrate this process
using interest rate spreads across countries, which re‡ect risk premia.
9
in each currency, using the expected growth in the marginal rate of substitution, and taking into account the cost (:). We de…ne the real exchange
rate as the ratio of …nal goods prices, expressed in common currency:
RERt =
S t Pt
:
Pt
(4)
Households rent capital to the …rms that produce intermediate goods.
Ktj 1 and Itj denotes holdings of capital stock and investment purchases, respectively. The real rental rate of capital is denoted by RtK : The capital
accumulation dynamics are given by the following expression
"
!#
Itj
j
j
Kt = (1
) Kt 1 + Vt 1 S
Itj ;
(5)
j
It 1
where denotes the rate of depreciation and the adjustment cost function,
S (:), is an increasing and convex function (i.e. S 0 (); S 00 () > 0). Furthermore,
in the steady state S = S = 0 and S 00 > 0: The S (:) function summarizes the
technology that transforms current and past investment into installed capital
for use in the following period. This expression also includes an investmentspeci…c technology shock (Vt ).
Households obtain labor income from supplying labor to intermediate
goods producers, for which they receive a nominal wage, Wtj , and receive
pro…ts from intermediate and wholesale …nal goods producers jt . As in
Erceg, Henderson, and Levin (2000; henceforth EHL), we assume that each
household is a monopoly supplier of di¤erentiated labor service, Ntj . The
household sells this service to a competitive …rm that transforms it into an
aggregate labor input. The labor input is used by the intermediate goods
producers. The elasticity of substitution across types of labor is "w . Households set wages in a staggered way with a Calvo-type restriction. In each
period, a fraction 1
w of households can reoptimize their posted nominal
wage. The assumption of complete markets within each country allows to
separate the consumption/saving decisions from the labor supply decision
(see EHL).
2.2
Firms
The model has …nal goods, di¤erentiated intermediate goods and composite
intermediate goods producers. Final goods producers purchase a composite
10
of intermediate home goods, YH;t , and a composite of intermediate foreignproduced goods, YF;t , to produce a homogeneous …nal good product. Intermediate di¤erentiated domestic and foreign goods producers operate under
sticky prices and monopolistic competition, and sell their products to intermediate domestic and foreign composite goods producers, who in turn sell
these to …nal goods producers. Composite intermediate goods are traded
across countries, while …nal goods are not.
2.2.1
Final good producers and “iceberg” costs
A continuum of …nal goods producers …rms purchase a composite of intermediate home goods, YH;t , and a composite of intermediate foreign-produced
goods, YF;t , to produce a homogeneous …nal good product. A fraction of
imported intermediate inputs are lost in transit between the two countries.
This functional form for transportation costs was …rst proposed by Samuelson (1954), and is also known in the literature as "iceberg costs". Therefore,
the production of the …nal good is given by:
n 1
1
Yt = ! YH;t + (1
1
!) [(1
1
) YF;t ]
o
1
;
(6)
where ! denotes the fraction of home-produced goods that are used for the
production of the …nal good, and denotes the elasticity of substitution
between domestically produced and imported intermediate goods in both
countries. The prices of these composite goods for the …nal good producers
are given by PH;t and PF;t . We can rewrite the weights as follows in the
production function of the …nal good:
h 1
1
Yt = ! YH;t + (1
1
! ) (YF;t )
1
i
1
;
(7)
where (1 ! ) = (1 !)(1 ) 1 . A higher rate of transportation costs , or
an increase in the elasticity of substitution decreases the value of (1 ! ),
and raises the home bias in the economy. In the Bayesian estimation of the
model we …x the parameter ! and then estimate and . The price level for
the …nal good is:
h
i11
Pt = ! (PH;t )1 + (1 !) (PF;t =(1
))1
;
where PH;t and PF;t denote the prices of the domestic and foreign intermediate
goods.
11
2.2.2
Intermediate Goods Producers
In each country, there is a continuum of intermediate di¤erentiated goods
producers, each producing a type of good that is an imperfect substitute
of the others, using domestic capital and labor. The elasticity of substitution across types of goods is "p . These di¤erentiated goods are sold to the
composite intermediate goods producers.
Technology The production function of each intermediate good h in the
home country is given by
Yt (h) = [At Nt (h) Xt ]1
[Kt
1
(h)] ;
(8)
where is the share of capital in the production function. The above production function has two technology shocks. The …rst one, Xt ; is a unit-root
world technology shock that a¤ects the two countries the same way. In addition, there is a labor-augmenting country speci…c technology shock, At ; that
evolves as a zero-mean, AR(1) process in logs.
Nominal Price Rigidities and Local Currency Pricing Once they
have solved for the optimal capital-output ratio and cost minimization, intermediate good producers choose the price that maximizes discounted pro…ts
subject to a Calvo-type restriction. In our baseline model, we assume local currency pricing (LCP) for goods that are shipped internationally: with
probability 1
H a …rm chooses a price for the domestic market and a price
for the foreign market, each price quoted in the destination market currency.
Hence, there is price stickiness in each country’s imports prices in terms of
local currency, and the law of one price (excluding iceberg costs) holds in the
steady state, but not outside of it. Additionally, we assume that the prices of
each …rm that cannot reoptimize in a given period is indexed to last period’s
in‡ation rate in each destination market with coe¢ cient H . Therefore, the
coe¢ cients of the two Phillips curves for each country (domestic in‡ation and
exports in‡ation) have the same coe¢ cients ( H , H ), but they di¤er across
countries. In the foreign country, foreign in‡ation and imports in‡ation are
governed by parameters ( F , F ).
12
2.3
Closing the Model
In order to close the model, we impose market-clearing conditions for all
types of home and foreign intermediate goods. For all aggregate intermediate goods, we need to take into account the size of the countries and the
transportation costs. A fraction of the exports is assigned to the transportation sector and the rest is demanded by the foreign country. For the
…nal good, the market clearing condition in the home country is the usual:
(9)
Yt = Ct + It + Gt :
We introduce an exogenous demand shock for each country (Gt ; Gt ) which
can be interpreted as government expenditure shocks that evolve as AR(1)
processes in logs. We assume that both governments run a balanced budget
every period (i.e. Gt = Tt and Gt = Tt ). Finally, we assume that both
countries follow a monetary policy rule that targets deviations of domestic
CPI in‡ation and real GDP growth from their steady-state values, that we
normalize to zero:
Rt
=
R
Rt 1
R
'R
[(Pt =Pt 1 )' (GDPt =GDPt 1 )'y ]
1 'R
exp("m
t );
(10)
where "m
t is an iid monetary policy shock.
3
3.1
Bayesian Estimation
Data
We estimate the model using quarterly data for the U.K. and the euro area,
between 1971 and 2008. The end-date is convenient to avoid the period
of zero interest rates and unconventional monetary policy measures in the
U.K., for which our model cannot provide a good characterization. We use six
domestic macroeconomic series per country, and the bilateral real exchange
rate, making a total of 13 observable variables. For each country we use:
real per capita GDP growth, real per capita consumption growth, real per
capita investment growth, real wage growth, CPI in‡ation and a short-term
interest rate.
Our data sources are as follows. For the euro area, we obtain real GDP,
real consumption, real investment, real wages, the Harmonized Index of Consumer Prices (HICP), and the short-term interest from the ECB’s Area Wide
13
Model (AWM). We obtain population series from Eurostat. Since this series
is annual, we use linear interpolation to transform it to quarterly frequency.
For the U.K. we obtain national accounts data (real GDP, real consumption
and real investment) from the O¢ ce for National Statistics. The relevant
measure for consumer prices is the Retail Price Index (RPI), obtained from
the O¢ ce for National Statistics. This series provides a longer time span than
the HICP (which is only available since 1995). For nominal wages, we use
average earnings for the whole economy (including bonus), also produced by
the O¢ ce for National Statistics. We compute real wages as nominal wages
divided by the RPI. We use the Bank of England’s Repo Rate as a measure
of short-term interest rates. Population for the U.K. is also obtained through
Eurostat, and transformed to quarterly frequency using linear interpolation.
Finally, for the bilateral measures, we construct the real exchange rate of
the U.K. pound sterling against the euro using the nominal exchange rate in
U.K. pounds per euro, and multiplying it by the HICP of the euro area and
dividing it by the RPI of the U.K.
3.2
Model Dynamics and Data Transformations
Since we have assumed that the model has a world technology shock with
a stochastic trend, then real output, consumption, capital, investment, real
wages, and the level of government spending inherit the same property and
are non-stationary in levels. In order to render these variables stationary in
the model, we divide them by the level of world technology. Real marginal
costs, hours, in‡ation, interest rates, the real exchange rate and all other
international relative prices are stationary. We obtain the model’s dynamics
by taking a log-linear approximation to the steady state values with normalized variables, zero in‡ation and balanced trade. We denote by lower case
variables percent deviations from steady state values. Moreover, variables
with a tilde have been normalized by the level of world technology to render
e e
et = Ct .
them stationary. For instance, for consumption, e
ct = CtCe C , where C
Xt
To estimate the model, we transform the series as follows. Since the
model has a productivity shock with a stochastic trend, real variables are
non-stationary in the model, but …rst-di¤erencing makes them stationary.
We apply the same treatment to their counterparts in the set of observable
variables, which is also enough to make them stationary. The relationship
between the same variable in the transformed model and in the data is as
14
follows. For real consumption, for example:
e
ct =
ct
"xt
where e
ct is consumption growth in the model and ct is consumption
growth in the data. The same reasoning applies to all other real variables.
To compute per capita real GDP, consumption and investment growth rates
we take logs and …rst di¤erences of the raw (per capita) data. To compute
real wage growth rates we also take logs and …rst di¤erences.
To compute in‡ation rates we also take logs and …rst di¤erences of the
relevant price level series. We use nominal interest rates in levels because they
are a stationary variable in the model and in the data. To make interest rates
quarterly, we divide them by 400. We use as observable variable the bilateral
real exchange rate in logs and …rst di¤erences. We demean all variables prior
to estimation.
Let denote the vector of parameters that describe preferences, technology, the monetary policy rules, and the shocks in the two countries of the
model. The vector of observable variables consists of {t = f gdpt ; gdpt ;
ct ; ct ; it ; it ; pt ; pt ; (wt pt ); (wt pt ); rt ; rt ; rert g. The
home country is the U.K. and the foreign country is the euro area. Hence
all variables and parameters with a star belong to the euro area. We express all variables as deviations from their sample mean. We denote by
L f{t gTt=1 j
the likelihood function of f{t gTt=1 :
3.3
Estimation: Priors and Posteriors
We employ standard Bayesian estimation techniques (An and Schorfheide,
2007). We specify priors over the model’s parameters ( ) and obtain the
posterior distribution of the parameters P
j f{t gTt=1 using the MetropolisHastings algorithm with 125,000 draws. To reduce the number of parameters
to be estimated, we …x a few parameters that are weakly identi…ed with the
set of observable variables (see Table 1).
15
Table 1: Calibrated Parameters
"w
"p
g=y
!
!
n
Value
0.99
0.025
0.36
1
6
11
0.2
0.9
0.975
0.2
Parameter
Discount factor
Depreciation rate
Capital share on the production of intermediate goods
Investment adjustment cost
Elasticity of substitution across types of labor
Elasticity of substitution across types of goods
Fraction of government spending in GDP
Degree of home bias in the U.K.
Degree of home bias in the E.M.U.
Size of the U.K.
We set the discount factor to = 0:995. The depreciation rate, ; is set
equal to 0:025 per quarter, which implies an annual depreciation on capital
equal to 10 percent. We set equal to 0:36. We set the adjustment cost of
investment, ; equal to 1; a standard value in the literature.18 We set the
elasticity of substitution across types of labor, "w ; and across types of goods,
"p ; equal to 6 and 11, respectively, as it is standard in the DSGE literature.
We set the steady-state ratio of government expenditures over GDP, equal
to 0:2: We set the fraction of imported goods, 1 !; equal to 0:10, which
is in line with the imports for the EMU/GDP ratio in the U.K. We set the
size of the U.K. economy to 0:2, based on the relative GDP sizes. Finally,
we calibrate ! , such that given the values of ! and n, trade between the
U.K. and the euro area is balanced. This value is quite similar to the ratio
of imports from U.K./euro area GDP in the data.
18
We estimated a version of the model where was estimated with a prior mean of 1.
The prior and posterior looked very much alike, suggesting that this parameter was not
identi…ed.
16
Table 2: Prior distributions
Parameters
b; b
;
H; F
H;
F
w; w
' ;'
' y ; 'y
' R ; 'R
c; c ; n;
a; a ; g ;
n
;
v;
v
;
Description
Habit persistence
Labor disutility
Elast. subst. between goods
Cost of foreign position
Cost of shipping goods
Calvo lotteries in prices
Indexation
Calvo lotteries in wages
Taylor rule In‡ation
Taylor rule output growth
Interest rate smoothing
AR(1) coe¢ cients of shocks
Gamma
Gamma
N ormal
Gamma
Gamma
Beta
Beta
Beta
N ormal
N ormal
Beta
Beta
Mean
0.7
1.0
1.5
0.02
0.10
0.66
0.50
0.75
1.5
1.0
0.5
0.75
Std. Dev.
0.05
0.25
0.25
0.014
0.05
0.1
0.2
0.1
0.25
0.2
0.28
0.2
Standard Deviation of Shocks
Preference
Investment and TFP
Government Spending
TFP Unit root shock
Uncovered Interest Parity
Monetary
Gamma
Gamma
Gamma
Gamma
Gamma
Gamma
1.0
0.7
1.0
0.7
1.0
0.4
0.5
0.3
0.5
0.3
0.5
0.2
g ; uip
("it ) ; i = c; c ; n; n
("it ) ; i = v; v ; a; a
("it ) ; i = g; g
("xt )
("uip
t )
("it ) ; i = m; m
The remaining parameters are estimated. Table 2 gives an overview of the
prior distribution of the estimated parameters, that we denote by ( ). We
use Beta distributions for parameters bounded between 0 and 1. For parameters assumed to be positive we use a Gamma distribution, and for unbounded
parameters we use normal distributions. We center the priors to values that
are typically used in calibrated exercises, or in previous estimations (such as
Smets and Wouters, 2003, for the euro area). For the transportation costs
we set = 0:10 as the mean prior, which is the estimate of transportation
costs for the U.S. calculated by Feenstra (1996) and Hummels (2001).
Posterior distributions for the structural parameters of the benchmark
economy are shown in Table 3, while Table 4 presents the posterior distributions related to the AR(1) coe¢ cients and standard deviations of the shocks.
Most parameter estimates are very similar to previous studies, in particu-
17
lar those of the euro area, so we brie‡y comment on them.19 Interestingly,
parameter estimates are not so di¤erent across the U.K. and the euro area,
suggesting that the economic structures are quite similar. This similarity
implies low costs of adopting a common currency. On the other hand, the
parameters of the shock processes are quite di¤erent, which suggests that if
they were to remain the same after a possible monetary union, then the costs
of not being able to respond to domestic shocks and allow the exchange rate
to absorb foreign shocks would be quite high.
The estimated posterior mean of the parameter ; that measures the
elasticity of the interest rate premium with respect to net foreign assets is
quite low, 0:0024, and hence suggests that the U.K. and the euro area enjoy
a high degree of …nancial integration. For instance, Rabanal and Tuesta
(2010) found an estimate between the U.S. and the euro area of 0:01 and
for emerging economies García-Cicco et al. (2010) …nd a value close to 3.
Next, we …nd that the elasticity of substitution between home and foreign
goods is below but close to one, with a posterior mean of 0:89: Finally, the
parameter measuring shipping costs of all sorts due to international trade
has a posterior mean of 0:089. This estimate implies that almost 9 percent
of the value of the goods traded internationally are spent on transportation
and other transaction costs.
The posterior mean estimates for the external habit formation parameters
are roughly in line with previous studies (b = 0:66 for the U.K. and 0:57 for
the euro area), while the same holds for the inverse elasticities of labor supply
( = 0:94 and
= 0:92). Our point estimates imply stronger nominal
rigidities in wage-setting than in price-setting: the posterior mean for the
Calvo lottery for price setting implies that prices are reset on average every
2 quarters, while wages are reset every 4 quarters both in the U.K. and
in the euro area. These estimates are somewhat lower than in Smets and
Wouters (2003) for the euro area. The posterior mean of the price indexation
parameter is much smaller than the mean value of the prior distribution, and
makes backward looking behavior negligible. Estimates of the Taylor rules
are also similar to what has been obtained in previous studies. We remark
once more that the parameter estimates are very similar across countries, and
hence the costs of monetary union would be coming from losing the capacity
to react to domestic and foreign shocks rather than di¤erences in the policy
reaction functions.
19
See Adolfson et al. (2007) and Rabanal and Tuesta (2010).
18
Table 3. Posterior distributions
b
0.66
b
0.57
(0.58- 0.75)
(0.52- 0.63)
0.94
0.92
(0.85- 1.05)
H
(0.85- 1.00)
0.50
F
0.16
F
0.78
w
(0.43 - 0.58)
H
(0.02 - 0.30)
w
(0.68 - 0.87)
'
1.06
'
0.75
'y
0.75
'R
(1.01 - 1.12)
'y
(0.60 - 0.89)
'R
(0.72 - 0.78)
0.89
0.52
(0.46 - 0.58)
0.12
(0.01 - 0.23)
0.79
(0.70 - 0.88)
1.15
(1.11 - 1.19)
0.54
(0.42 - 0.67)
0.78
(0.75 - 0.81)
0.002
(0.80 - 0.98)
(0.0001 - 0.004)
0.089
(0.02 - 0.15)
Table 4. Posterior distributions, shocks parameters
c
n
v
("ct )
("nt )
("vt )
("uip
t )
0.39
c
0.76
n
0.47
v
3.34
"ct
6.88
"nt
4.76
"vt
0.32
("xt )
(0.19 - 0.58)
(0.68 - 0.84)
(0.34 - 0.60)
(2.55 - 4.04)
(5.56 - 8.19)
(4.19 - 5.31)
(0.17 - 0.47)
0.97
a
0.98
g
0.96
uip
1.92
("at )
3.51
("gt )
1.04
("m
t )
(0.96 - 0.99)
(0.96 - 0.99)
(0.93 - 0.99)
(1.40 - 2.44)
(2.70 - 4.27)
(0.91 - 1.15)
0.92
a
0.89
g
(0.87 - 0.98)
(0.85 - 0.93)
0.99
(0.99 - 0.99)
0.96
(0.94 - 0.98)
0.92
(0.88 - 0.96)
2.37
"at
5.69
("gt )
0.36
"m
t
(1.94 - 2.80)
(5.20 - 6.17)
(0.31 - 0.40)
1.36
(1.15 - 1.59)
1.73
(1.56 - 1.90)
0.21
(0.18 - 0.24)
0.36
(0.18 - 0.54)
Table 4 shows that the shocks processes are quite di¤erent across countries. In particular, preference shocks and investment-speci…c shocks are
more persistent in the euro area than in the U.K., while the innovations to
the shocks are larger in the U.K. for those shocks. The TFP and government
spending shock processes are quite similar across countries, while monetary
policy shocks are …fty percent more volatile in the U.K. than in the euro
area. In order to better understand how well the model …ts the data and
what shocks in the model drive which variables, Table 5 presents posterior
19
distributions for the standard deviation of the observable variables implied by
the model, as well as their variance decomposition. In the data, the U.K. is
more volatile than the euro area. In particular, real per capita consumption
and GDP growth is twice as volatile than in the euro area, while investment
is almost four times as much. In‡ation, real wage growth and nominal interest rate are also more volatile in the U.K. than in the euro area. The
model is able to replicate these facts qualitatively, although it overpredicts
the volatility of some real variables, in particular real GDP growth in both
countries, investment in the euro area, and the real exchange rate.
Next, we analyze which shocks drive the behavior of the main variables (Table 5). We have aggregated the shocks as: supply (including TFP
and investment-speci…c technology shocks in both countries), preference (intertemporal and intratemporal shocks in both countries), government spending, monetary (also aggregated across countries), and the UIP shock. First,
we …nd the usual “exchange rate disconnect”, in the sense that RER ‡uctuations are driven by the UIP shock (63.6 percent of its variance is driven
by this shock), while the UIP shock explains very little of the volatility of
all other macro variables. Supply disturbances explain about 19.2 percent of
the volatility of the RER, while monetary shocks explain about 10 percent.
Second, monetary policy shocks explain an important fraction of the variance of in‡ation (about 18 percent in both the U.K. and the euro area), and
they explain also about 10 percent of the volatility of real GDP, consumption
and investment growth in the euro area. The importance of monetary policy
shocks in explaining the volatility of real variables in the U.K. is smaller
(around 5 percent). Third, government spending shocks represent a signi…cant fraction of real GDP growth volatility in the U.K. (22.4 percent) while
they are a smaller fraction in the euro area.
Finally, it is worth mentioning that each variable is primarily driven
by one or two types of shock. For instance, investment is driven mostly
by investment-speci…c technology shocks, consumption is driven by the intertemporal preference shock, and real wages are driven by the TFP and
the intratemporal preference shock. These results are consistent with other
DSGE model estimations such as Justiniano et al. (2010) and Rabanal and
Tuesta (2010). While not shown explicitly in Table 5, the fraction of variance
for each variable explained by shocks in the other country is always negligible:
the international transmission of shocks is fairly small in the model.
20
Table 5. Second Moments
Standard Deviations
gdp
Data
0.94
gdp
0.59
c
1.07
c
0.56
i
5.61
i
1.37
p
1.38
p
1.23
(w
(w
p)
p)
1.11
1.07
r
0.89
r
0.86
(rer)
3.32
Variance Decompositions
Model
1.83
Supply
Pref.
Govt. Sp.
Mon.
UIP
56:7
13:6
22:4
6:7
0:4
0.93
47:3
31:7
8:0
12:9
0:1
1.28
14:1
75:3
2:8
6:6
1:2
0.85
41:2
46:1
2:8
9:7
0:2
5.94
84:0
9:3
1:1
4:0
1:7
2.31
56:7
31:5
0:4
10:5
0:7
1.52
50:7
15:5
10:2
18:6
5:0
0.96
34:2
45:2
2:7
17:3
0:5
1.09
46:7
48:9
0:7
0:4
3:3
0.68
65:4
33:0
0:4
0:6
0:5
1.01
55:9
13:5
19:5
3:6
7:6
0.84
31:1
62:6
3:9
1:9
0:4
4.39
19:2
6:6
0:7
9:9
63:6
(1.71- 1.93)
(0.85- 1.01)
(1.16- 1.37)
(0.80- 0.91)
(5.36-6.41)
(2.05- 2.52)
(1.27- 1.71)
(0.79- 1.08)
(0.98- 1.18)
(0.62- 0.73)
(0.77- 1.21)
(0.64- 1.01)
(3.87- 4.76)
Note: “Supply" includes TFP and IST shocks, “Pref." includes intertemporal
and intratemporal utility shocks.
4
Policy Analysis: Welfare Gains of Entering
a Monetary Union
This section uses the estimated model to evaluate under what conditions will
the U.K. bene…t from joining the euro area. As we discussed in the introduction, we emphasize three factors that will impact the welfare of households
in the U.K.:
1. The loss of independent monetary policy in a monetary union: entering a monetary union increases output and in‡ation volatility because
21
monetary conditions in the EMU as a whole will not generally …t U.K.
needs. The additional volatility generated by losing an independent
monetary policy results in welfare losses.
2. The increase of trade due to lower transaction costs: the empirical
literature …nds that there is an expansion in trade for the country that
joins a currency area (Rose, 2008). It is not clear what the precise
magnitude of this trade expansion is. In the welfare analysis, we model
the trade expansion as a reduction in trade costs. In our model, this
re‡ects all possible transactions costs related to trade. This is a steadystate e¤ect that will increase consumption and production in the U.K.
Its e¤ects on volatility are quantitatively very small.
3. Changes in the behavior of UIP shocks that can occur in a monetary
union. If one where to study the behavior of the UIP shock between
1999-2007 for those countries in the euro area, one would conclude that
these shocks are fairly small. But the experience since 2007 is that we
cannot rule out the presence of this shock, and both the level and the
volatility cannot be assumed to be zero after EMU membership. If
either the mean or the volatility this shock increase, welfare will be
a¤ected negatively in the U.K.
We adopt a conservative approach and assume that the transaction costs
(or “iceberg costs”as de…ned in section 2) drop by 5 percentage points. This
value is at the lower end of estimated trade costs reductions for joining the
EMU (see Anderson and van Wincoop, 2004). We calibrate the change in
the mean and variance of the risk premium, assuming that the U.K. will
experience an increase in the risk premium similar to the average of France,
Italy, and Spain. Excluding Germany, these economies are the largest in the
euro area, and are close in size to the U.K.20 Since there is high uncertainty
about how trade costs and the risk premium will behave for the U.K. once it
enters the EMU, we conduct an extensive sensitivity analysis for alternative
parameter values in section 6.
20
An alternative scenario for the U.K. is one in which its …nancial assets are considered
as a safe haven by international investors and the risk premium declines. We evaluate the
impact of this scenario on welfare in the sensitivity analysis section.
22
We calculate the welfare gains of joining a monetary union following the
1
same approach by Lucas (1987). Given a set of allocations Ctk ; Ntk t=0 for
k = I; M U , where I is the allocation under the independent monetary policy
and M U the allocation under the monetary union, the welfare gain is
calculated as follows:21
"1
#
"1
#
X
X
t
t
E
u((1 + )CtI ; NtI ) = E
u(CtM U ; NtM U )
(11)
t=0
t=0
If the resulting parameter is positive, then there are net gains from
entering a monetary union. On the other hand if < 0, then a country is
better o¤ following an independent monetary policy. We calculate the welfare
gain for two cases. First, we calculate the welfare gain at the steady state
to understand the long-run e¤ects of joining a currency area. Second, we
measure the e¤ects of changes in the business cycle (i.e. volatility of main
variables) on welfare.
Table 6 shows the steady-state e¤ects and welfare gains of joining a currency area under lower trade costs and under increased …nancial turbulence.
In the …rst column, we show the steady state values, which are normalized to
100, under the current situation (independent monetary policy and ‡exible
exchange rate). In the second column, we show the long-run e¤ect of lower
transaction costs. The overall e¤ect is an increase in welfare of 1.2 percentage points of life-time consumption. The reduction of trade costs has several
e¤ects in the economy. First, it allows the U.K. economy to trade more: the
reduction of trade costs leads to an increase in 0.2 percentage points in both
exports and imports. Second, households have more resources available due
to lower transaction costs, and hence consumption will be higher. Also, as a
result of wealth e¤ects, labor supply will decrease. Third, lower distortions
will lead to higher investment, capital stock and GDP. The impact on consumption and leisure determines an increase in welfare at the steady state.
Finally, the U.K. enjoys a safe haven status where the average risk premium
is zero.
The third column of Table 6 illustrates the case of …nancial turbulence by
assuming an increase of the average UIP shock by 40 basis points (quarterly).
This is the di¤erence in the interest rate spread of the U.K. and the average
of France, Italy, and Spain for the (crisis) 2008-2011 period. This scenario is
21
The welfare cost estimate comes from the unconditional expected lifetime utility, and is
calculated up to a second order approximation following Schmitt-Grohé and Uribe (2007).
23
intended to evaluate the impact of adopting a common currency in times of
…nancial stress, and for which there would be no use of unconventional monetary policy in the U.K. There are several e¤ects of a higher mean of the UIP
shock. First, higher interest rates a¤ect negatively the decision on consumption and investment, which lead to a decline in GDP. Second, the negative
wealth e¤ect increases labor supply, but the e¤ect is quantitatively small.
Finally, the decline in real wages leads to a real exchange rate depreciation,
which in turn increases exports and reduces imports.
Table 6. Steady State E¤ects and Welfare Gains
Variables in Levels
Output (gdp)
Consumption (c)
Investment (i)
Capital (k)
Employment (n)
Exports (x)
Imports (m)
W elf are Gains (
Ind. M.P.
M.U.
Low T.C.
M.U.
High UIP.
100
100
100
100
100
100
100
100:71
100:92
100:71
100:71
99:89
100:21
100:21
99:93
99:90
99:97
99:97
100:04
100:34
99:97
100)
1:20
0:21
Note: All the variables are reported in levels except the welfare gain, which is
expressed as a percentage of steady state consumption. The macroeconomic
variables with an independent monetary policy are normalized to 100. "Ind
M.P." means Independent Monetary Policy. "M.U." means Monetary Union.
"Low T.C." means low transportation costs scenario.
These experiments illustrate the long-run e¤ects of two possible scenarios
after the adoption of a currency union. On the one hand, there are large
positive e¤ects coming from a reduction of trade costs, and a safe haven
status. But, if the U.K. experiences higher …nancial turbulences, there would
be negative e¤ects associated with higher average interest rates. However,
these results abstract from the cyclical e¤ects of joining a currency union.
Under a common currency, there is a loss of monetary independence and
exchange rate ‡exibility, which limits the ability of a country to stabilize the
24
cycle and respond to shocks. If the cycle is not perfectly synchronized with
the rest of the member countries of the currency union, and wages and prices
are sticky, then the adjustment will involve more macroeconomic volatility in
real variables. This volatility e¤ect can undermine the bene…ts derived from
lower transaction costs or magnify costs of a higher UIP shock.
Table 7 shows the business cycle e¤ects of alternative monetary and exchange rate policy arrangements. In the …rst column, we compute the volatility of main U.K. variables under the baseline model with both the ECB and
the BoE following their estimated Taylor rules. Then, we compare this baseline scenario with four alternative policy scenarios. The second column shows
the case when the U.K. joins the EMU and transaction costs remain high. In
this case, there is an increase in volatility of most macroeconomic variables
due to the fact there is no ‡exible nominal exchange rate and domestic interest rate policy to absorb country-speci…c shocks in the U.K. Only exports
and real exchange rate volatility decline. In the model, the real exchange
rate is less volatile because the external adjustment of the economy is done
via prices, which adjust slowly overtime. A lower volatility of the exchange
rate will also reduce the volatility of exports in the model. The welfare loss
derived exclusively from entering the monetary union will be 0.3 percent
of life-time consumption, which is fully explained by higher macroeconomic
volatility.
25
Table 7. Business Cycle E¤ects and Welfare Gains
Variables in First
Di¤erences
Ind. M.P.
M.U.
High T.C.
M.U.
Low T.C.
M.U.
Low UIP
M.U.
High UIP
Output ( gdp)
Consumption ( c)
Investment ( i)
Capital ( k)
Employment ( n)
Exports ( x)
Imports ( m)
Consumer Price ( p)
Real Exchange Rate ( rer)
1:83
1:28
5:94
0:61
3:07
3:19
1:98
1:52
4:39
2:14
1:51
7:20
0:68
3:66
1:38
2:42
1:58
1:28
2:14
1:51
7:20
0:68
3:66
1:38
2:42
1:58
1:28
1:72
1:29
5:87
0:59
3:06
1:17
1:91
1:05
1:41
4:17
2:67
13:78
1:17
6:74
2:45
4:86
2:56
2:27
0:20
3:90
W elf are Gains (
100)
0:26
0:26
See notes in Table 6.
The third column of Table 7 shows the case when the U.K. joins the
EMU, reducing transaction costs by 5 percentage points. Consistent with
the work of Ravn and Mazzenga (2004), the cyclical e¤ects of a reduction in
transaction costs are very small in the model.22 The fourth column describes
the situation in which the UIP shocks disappear once the U.K. joins the
EMU. This scenario captures the episode of interest rate spreads compression observed in the period 1999-2007 for several EMU members, and would
re‡ect that the U.K. becomes a safe haven with no risk premia. Removing
UIP shocks reduces output growth volatility and leads to a welfare gain of
0.2 percent of life-time consumption. Finally, the …fth column shows the
case when the U.K. enters the EMU in a situation of …nancial turbulence.
We calibrated a situation of …nancial turbulence by increasing the standard
deviation of UIP shocks three times. This scenario is consistent with what
happened with France, Italy and Spain relative to the U.K. in the recent
…nancial crisis. As a result, the volatility of domestic interest rates increases
importantly, which transmits to most macroeconomic variables. The only
22
The quantitative e¤ects on business cycles are noticeable when the reduction in transaction costs is greater than 50 percent. With a reduction of only 5 percent, the results in
columns 2 and 3 in table 7 are virtually the same.
26
exception is the real exchange rate. As explained in the previous paragraph,
lower exchange rate volatility can be explained by price rigidities which turns
the external adjustment much more slower compared to the case of a ‡exible
exchange rate. This scenario leads to a welfare loss of 3.9 percent of life-time
consumption.
We have just studied the e¤ects of UIP shocks and their detrimental
e¤ect on welfare when the U.K. joins the euro. But what are the dynamics
of a UIP/interest rate spread shock when the U.K. does not enter the euro
area? In Figure 4 we present the impulse-responses to a UIP shock, under an
independent monetary policy with ‡exible exchange rates and under EMU
membership. The e¤ects are strikingly di¤erent. In panel F we observe that,
in a monetary union, the UIP shock translates into an increase in the interest
rate in the U.K., while in the case of an independent monetary policy the UIP
shock a¤ects both interest rates and exchange rates. Inside the EMU, the UIP
shock acts as a monetary shock, and hence depresses output, employment and
in‡ation (Panels A and B). On the contrary, under a ‡exible exchange rate,
the UIP shock translates mostly into a depreciation of the currency, and to
some interest rate increases. As a result, the overall e¤ect on output and
in‡ation is negligible. It is important to note that, in a monetary union,
the depreciation process is more sluggish. Panel E shows that in fact, the
real exchange rate devaluation in a monetary union is implemented with a
de‡ation, a process that is typically described as an "internal devaluation".
Clearly, if UIP shocks are important, enjoy exchange rate ‡exibility allows
to o¤set their contractionary e¤ects.
Table 8 summarizes the main results from this section combining the
steady state and business cycle e¤ects. First, in tranquil times and under
lower transaction costs, there are positive gains from entering a monetary
union of 0.9 percent of life-time consumption. Second, under …nancial turbulence the result is completely reversed, and belonging to a monetary union
generates a net welfare loss of 2.9 percent. This stark di¤erence in the results
can help to rationalize the decision of the U.K. to postpone the entry to the
EMU. During tranquil times the model indicates substantial bene…ts from
adopting a currency, however under …nancial turbulence the gains disappear
and the appropriate regime is to stay out of the EMU.
27
Table 8. Summary of Welfare Gains
(Percentage points of life-time consumption)
Steady State E¤ects
Trade Costs
Interest Rate Spread
Business Cycle E¤ects
Monetary Union - Historical Shocks
Monetary Union - Volatile Spread Shocks
Financial
Turbulence
1:20
1:20
0:99
1:20
0:21
0:26
0:26
3:90
3:90
0:94
Aggregate E¤ects
5
Tranquil
Times
2:91
Sensitivity Analysis
Given the uncertainty on how parameter values will behave before and after
EMU membership, in this section we present some sensitivity analysis. As
we discussed in the previous section, if the only change in environment is
that the UK enters the EMU, there is a welfare loss of 0.26 percent of lifetime consumption, due to the loss of monetary and exchange rate policy. We
consider the impact on welfare of changing some key parameters of the model
in Figure 5, including: (i) a reduction in transaction costs, (ii) changes in
the probability of a …nancial crisis, (iii) changes in the mean of the steadystate interest rate spread, (iv) changes in the standard deviation of the UIP
shock, that a¤ect the volatility of interest rates, (iv) changes in the degree
of nominal price rigidities, and (vi) changes in the degree of wage rigidities.
Panel A shows welfare gains as a function of trade costs. Under the
baseline scenario trade costs fall to 4 percent and the welfare gains of joining
a monetary union are close to 1 percent. However, if after joining the currency
area there is no reduction in trade costs, and these remain at 9 percent, then
the U.K. will experiment a welfare loss of 0.26 percent of GDP.23 The cut-o¤
23
Santos Silva and Tenreyro (2010) show that the euro e¤ect on trade has been close to
zero. Using their estimate our model will show a net welfare loss derived from entering a
monetary union.
28
point for a welfare improvement with respect to trade costs is 8 percent.
Panels B and C show the e¤ects of changing the mean and the standard
deviation of the UIP shock. Setting the mean of the UIP shock raises steadystate interest spreads by the same amount. Increasing interest rate spreads
to 40 basis points increases the welfare costs but to a limited extent. On the
other hand, a reduction in the mean spread (which could also be possible
if …nancial markets view U.K. debt as safe haven) would lead to a positive
welfare gain from entering the EMU. Panel D describes the impact of the
volatility of UIP shocks on welfare. The quantitative e¤ect of increasing
the standard deviation of the UIP shock is much larger than increasing the
mean. In the baseline model, the standard deviation of the UIP shock is 0.3,
and generates a welfare cost of 0.3 percentage point of life-time consumption.
In an scenario similar to the recent crisis episode, the risk premium volatility increases 3 times then the welfare cost raises to 4 percent of life-time
consumption.
Panel D shows the e¤ects of changing the probability of a …nancial crisis
on welfare. In the case where the probability is 1, we obtain the same results
as in the previous section and the net welfare costs on joining the monetary
union are 2.9 percentage points of life-time consumption. As we reduce the
probability of a crisis, then the welfare costs are lower. In the extreme case
of having a zero probability of a …nancial crisis, that is a macroeconomic
scenario for tranquil times, we obtain a net welfare gain of 0.9 percentage
points of life-time consumption. When the probability of a crisis is 0.25, then
all the bene…ts of lower trade costs are fully o¤set by the costs of higher
macroeconomic volatility, and the country is indi¤erent between joining a
monetary union and adopting an independent monetary policy.
Panel E shows the e¤ect of price stickiness on welfare. In the baseline
model, the estimated Calvo parameter is close to 0.5, which implies an average frequency of price adjustment of 2 quarters. Reducing the frequency of
price adjustment in the economy does not increase welfare substantially, because in the baseline model price rigidities are small already. However, Panel
F shows that there are larger welfare gains from reducing wage rigidities. In
the baseline model, the wage rigidity Calvo parameter is close to 0.8, which
implies a frequency of price adjustment greater than four quarters. Reducing
the frequency to three quarters or less, can generate a positive welfare gain
of EMU membership, even without assuming a reduction in trade costs.
In this section we described how the welfare analysis changes in response
to di¤erence assumptions on the parameters of the model. Two important
29
results emerge from this analysis. First, the welfare gain from entering a
monetary union can be completely eliminated with …nancial shocks similar
in size and volatility to what has been observed in the recent …nancial crisis
episode. Second, there are some potential gains from increasing labor market
‡exibility. If a government implement labor market reforms that increase
the ‡exibility of the economy, it could more than compensate the lack of the
nominal exchange rate adjustment over the business cycle.
6
Conclusions
This paper revisits the old issue of optimal currency areas. Since the seminal paper by Mundell (1961) on optimum currency areas, there has been an
extensive research on bene…ts and costs of joining a monetary union. Even
though a complete analysis of entering a currency union should include several dimensions in terms of the impact on growth and business cycles, we
contributed to the discussion in two dimensions. First, we estimated a twocountry DSGE model of the U.K. and the euro area in order to use it as a
laboratory to evaluate the welfare impact on the U.K. of adopting the euro.
Second, we evaluate the role of trade and …nancial channels in the decision
of entering a monetary union.
On the one hand, joining a currency union could reduce the transaction
costs of trade with other countries, providing e¢ ciency gains to the new
member country and the monetary union as a whole. On the other hand,
adopting a common currency is costly for a country since it loses independent
monetary and exchange rate policies as tools for macroeconomic stabilization.
The paper shows that when comparing these two channels only, the trade-o¤
is resolved in favor of entering the euro area with a net welfare gain of 0.9
percentage points of life-time consumption.
However, the …nancial channel can radically change the welfare implications of entering a monetary union. Under the baseline parametrization, introducing …nancial shocks of the magnitude observed in the current …nancial
crisis can eliminate any potential gain from lower trade costs. In particular,
the welfare costs from an episode of …nancial turbulence is more than three
times the welfare gains derived from lower trade costs. The policy analysis underscores the fact that …nancial stability, measured as low and stable
risk premium, is of key importance to sustain a monetary union. Interest
rate spread shocks might eliminate any potential gain from entering into a
30
currency area.
Throughout the analysis, we have treated spread shocks as exogenous,
but there are reasons to think that they are not. To the extent that spreads
di¤er across countries because of di¤erent underlying fundamentals and as
a discipline device, di¤erences should be welcome. The increased …nancial
turbulence in the EMU is likely to be a by-product of the design ‡aws in the
creation of the single currency, and include failures in …scal discipline, lax
regulatory policies and a disregard for persistent current account imbalances
in the EMU. Therefore, European policymakers should aim at reducing the
incidence of these factors by ensuring that the right policies are implemented
in the future. Also, during the crisis, the BoE has conducted unconventional
monetary policies that reduced the level and volatility of U.K. long term
rates. This capability would be lost if the U.K. entered the EMU, although
the ECB has also provided ample liquidity in the markets through commercial banks using long-term re…nancing operations (LTRO). Possibly, the way
forward inside the EMU is to enforce the right policies to reduce …nancial turbulences in the markets and contagion, and to make sure that countries have
enough …scal space to conduct countercyclical …scal policy in the midst of a
crisis. The paper also illustrated how the lack of exchange rate adjustment
in a monetary union can be more than compensated with wage ‡exibility.
Introducing reforms in the labor market that ensure rapid wage adjustment
over the cycle can also help to preserve the gains from a monetary union.
There are several interesting extensions for future research. First, we can
consider the impact of uncertainty shocks into the model. Not only there is
an impact on the risk premium, but also on uncertainty about the futures
prospects of …scal solvency. We could introduce volatility shocks to the interest rate as in Fernández-Villaverde et al. (2011) to measure the e¤ects of
uncertainty in the euro area. Second, we could model unemployment frictions. The sudden rise of unemployment during the great recession, and the
subsequent slow recovery could be model through the Mortensen-Pissarides
framework as in Shimer (2010). Finally, given the importance of …nancial
services on the U.K. economy (around 10 percent of GDP), it would be useful
to model explicitly the …nancial system to quantify the impact of entering
the euro area.
31
A
Appendix: The Model
In this appendix we present the stochastic two country model that we will use
to analyze linkages between the U.K. and the euro area. We estimate a twocountry version of a DSGE model similar to those by Christiano, Eichenbaum
and Evans (2005) and Smets and Wouters (2003, 2007), where we include
trade and …nancial linkages across countries. A similar two-country model
has been estimated by Rabanal and Tuesta (2010) using data for the United
States and the euro Area. As in that paper, our benchmark model assumes
that there is local currency pricing for goods that are shipped internationally.
In addition, we assume that there is an incomplete asset market structure at
the international level: agents only have access to one non-contingent bond
that is denominated in foreign-country currency. The model incorporates 14
shocks because in the econometric section we are interested in explaining 13
variables.
We assume that there are two countries, home and foreign, of sizes n
and 1 n, respectively. Each country produces a continuum of intermediate
goods, indexed by h 2 [0; n] in the home country and f 2 [n; 1] in the foreign
country, which are traded internationally. Intermediate goods are imperfect
substitutes for each other, and are priced according to a Calvo-type restriction. They are used as in input in the production of the …nal good that is
used for domestic …nal consumption, investment, and government spending,
and hence it is not traded across borders. The model also incorporates linear
shipping costs of moving goods internationally. As it is typically done in
the literature, we follow Samuelson (1954) and introduce "iceberg" shipping
costs.
In what follows, we present the problem for households, intermediate
goods producers, shipping …rms, and …nal goods producers in the home country. The expression for the foreign country are analogous, and the convention
we use is that variables and parameters with an asterisk denote the foreign
country counterparts.
A.1
Households
In each country, there is a continuum of in…nitely lived households in the unit
interval, that obtain utility from consuming the …nal good and disutility from
supplying hours of labor. In the home country, households are indexed by j
2 [0; n] and their life-time utility function is:
32
E0
1
X
t
"
Dc;t log
t=0
Ctj
bCt
1
Dn;t
Ntj
1+
1+
#
(12)
;
where E0 denotes the rational expectations operator using information
up to time t = 0. 2 [0; 1] is the discount factor. Consumers obtain utility
from consuming the …nal good, Ctj , with external habit formation. b 2 [0; 1]
denotes the importance of the habit stock, which is last period’s aggregate
consumption (Ct 1 ).
> 0 is the inverse elasticity of labor supply with
respect to the real wage, and Ntj is the labor supply of the household. Dc;t ;
and Dn;t denote intertemporal and intratemporal preference shocks.24 These
shocks evolve as follows:
A.1.1
log(Dc;t ) =
c
log(Dc;t 1 ) + "c;d
t ;
log(Dn;t ) =
n
log(Dn;t 1 ) + "n;d
t :
International Asset Markets Structure and the Budget Constraint
Markets are complete within each country and incomplete at the international level. We introduce international incomplete markets in a simple and
tractable way, following Benigno (2009). We assume that, in each country,
domestic households have access to a nominal riskless bond that costs the
inverse of the gross domestic nominal interest rate. Given the assumption of
complete markets, this bond is redundant. In addition, there is an internationally traded bond that is denominated in foreign country currency, and
that allows to engage in intertemporal international trade across countries.
The budget constraint of home-country households is given by:
Pt Ctj + Itj +
= Btj
24
1
+ St Dtj
1
Btj
+
Rt
Rt
St Dtj
St Dt
Yt Pt
+ Wtj Ntj + Pt RtK Ktj
See Primiceri et al. (2006).
33
(13)
+ Tt
Ut
1
+
j
t
+
j
t;
where Btj and Dtj denote holdings of the domestic and foreign currency
denominated bonds, Rt is the home country gross nominal interest rate and
Rt is the foreign country gross nominal interest rate. St is the nominal
exchange rate expressed in units of domestic currency needed to buy one
unit of foreign currency and Pt is the price level of the …nal good (to be
de…ned below). Tt are lump-sum taxes that are used to …nance government
spending. jt denotes the payo¤ from engaging in trade of domestic statecontingent securities.25
Home-country households also face a cost of undertaking positions in the
foreign bonds market. The (:) function captures this cost and depends on
the aggregate real holdings of the foreign assets in the entire economy, and
therefore is taken as given by individual households.26 We also include an
exogenous shock (Ut ) to the function (:), which helps explains deviations
from the uncovered interest rate parity condition. For this reason, we call
this shock the "uncovered interest rate parity" shock, which also follows a
zero mean, AR(1) process in logs.
Consumers obtain labor income from supplying labor to intermediate
goods producers, for which they receive a nominal wage, Wtj , and receive
pro…ts from intermediate and wholesale …nal goods producers jt . The model
includes sticky wages, and hence the wage received by each household is speci…c and depends on the last time wages were reoptimized. The assumption
of complete markets within each country allows to separate the consumption/saving decisions from the labor supply decision (see Erceg, Henderson,
and Levin, 2000; henceforth EHL).
A.1.2
Capital Accumulation and the Investment/Savings Decision
Households rent capital to the …rms that produce intermediate goods. Ktj 1 and
Itj denotes holdings of capital stock and investment purchases, respectively.
The real rental rate of capital is denoted by RtK : The capital accumulation
dynamics is given by the following expression
25
In order to keep notation simple, we do not make the structure of the complete domestic asset markets explicit.
26
This cost induces stationarity in the net foreign asset position. See Schmitt-Grohé
and Uribe (2003) for applications in small open economy models, and Benigno (2009) in
two-country models.
34
Ktj = (1
) Ktj
1
"
+ Vt 1
Itj
Itj 1
S
!#
Itj :
(14)
Here, denotes the rate of depreciation and the adjustment cost function,
S (:), is an increasing and convex function (i.e. S 0 (); S 00 () > 0). Furthermore,
in the steady state S = S = 0 and S 00 > 0: The S (:) function summarizes the
technology that transforms current and past investment into installed capital
for use in the following period. This expression also includes an investmentspeci…c technology shock (Vt ) that evolves as:
log(Vt ) =
v
log(Vt 1 ) + "vt :
The …rst order conditions for holding domestic and foreign bonds, capital
and investment are:
Ct bCt 1 Dc;t+1 Pt
Ct+1 bCt Dc;t Pt+1
1 = Rt Et
St Dt
Pt Yt
1 = Rt
Qt = Et
1
=
Ct bCt 1 Dc;t+1 St+1 Pt
Ct+1 bCt Dc;t St Pt+1
Ct bCt 1 Dc;t+1
Ct+1 bCt Dc;t
Qt Vt 1
Et
ut Et
S
It
It
K
Rt+1
+ Qt+1 (1
It
1
Ct bCt 1 Dc;t+1
Ct+1 bCt Dc;t
(15)
;
It
S
1
(16)
;
)
(17)
;
It
I
"t
Qt+1 Vt+1 S
(18)
1
0
It+1
It
It+1
It
2
#
;
where Qt is the shadow price of investment in terms of consumption goods,
and where we have dropped all the superscripts, since by using the domestic
complete markets assumption, all households in one country take the same
decision. Combining equation (16) with the analogous to (15) in the foreign
country delivers the following risk-sharing condition, which forms the basis
of the real exchange rate determination under incomplete markets:
Et
Ct b Ct 1 Dc;t+1 Pt
Ct+1 bCt Dc;t Pt+1
= Et
Ct bCt 1 Dc;t+1 St+1 Pt
Ct+1 bCt Dc;t St Pt+1
35
S t Dt
Ut :
Yt Pt
(19)
We de…ne the real exchange rate as the ratio of …nal goods prices, expressed in common currency:
S t Pt
:
Pt
RERt =
A.1.3
(20)
Staggered Wage Setting and The Wage Decision
As in EHL, we assume that the household is a monopoly supplier of di¤erentiated labor service, Ntj . It sells this service to a competitive …rm that
transforms it into an aggregate labor input that is used by the intermediate
goods producers. Thus, one e¤ective unit of labor that an intermediate goods
producer …rm, h, uses for production is given by
1
n
Nt (h) =
"w
Z
n
Ntj (h)
"w 1
"w
"w
"w 1
dj
(21)
;
0
where Ntj (h) is the amount of labor supplied by household j to …rm h.
As shown by EHL, the demand curve for each type of labor is given by
! "w
j
W
t
Nt ; for j 2 [0; 1];
(22)
Ntj =
Wt
where Wt and Nt are aggregate labor and wage indices as follows: Wt =
1
Z n
1 "w
R
R
1
"
w
j
j
j
1
1 n
1 n
;
N
W
dj
=
N
Nt (h)dh.
(h)dh;
and
N
=
t
t
t
t
n
n 0
n 0
0
Households set wages in a staggered way with a Calvo-type restriction.
In each period, a fraction 1
w of households can reoptimize their posted
nominal wage. Consider a household resetting its wage in period t, and let
Wt the newly set wage. The household will choose Wt in order to maximize
M axEt
Wt
1
X
k=0
(
k
w)
"
Dc;t+k log (Ct+k
bCt+k 1 )
Dn;t+k
Nt+kjt
1+
1+
#
; (23)
where Nt+kjt denotes labor supply in period t + k of a household that
last reset its wage in period t. Households maximize (23) subject to (13)
and (22): The …rst order condition associated with the problem above can
be expressed as follows:
36
Et
1
X
k=0
(
k
w)
Dc;t+k Nt+kjt
(Ct+k bCt+k 1 )
Wt
Pt+k
"w
"w
1
Dn;t+k Nt+kjt (Ct+k
bCt+k 1 )
(24)
Wt
( Wt+k
) "w Nt+k :
where Nt+kjt =
The evolution of the aggregate wage index is given by
Wt =
A.2
1 "w
w Wt 1
+ (1
w ) (Wt
)1
"w
1
1 "w
(25)
:
Firms
The model has …nal goods, di¤erentiated intermediate goods and composite
intermediate goods producers. Final goods producers purchase a composite
of intermediate home goods, YH;t , and a composite of intermediate foreignproduced goods, YF;t , to produce a homogeneous …nal good product that is
non-tradable across countries. Intermediate di¤erentiated domestic and foreign goods producers operate under sticky prices and monopolistic competition, and sell their products to intermediate domestic and foreign composite
goods producers, who in turn sell these to …nal goods producers. Composite
intermediate goods are traded across countries.
A.2.1
Final good producers and “Iceberg” costs
A continuum of …nal goods producers …rms purchase a composite of intermediate home goods, YH;t , and a composite of intermediate foreign-produced
goods, YF;t , to produce a homogeneous …nal good product. A fraction of
imported intermediate inputs are lost in transit between the two countries.
This functional form for transportation costs was …rst proposed by Samuelson (1954), and is also known in the literature as "iceberg costs". Therefore,
the production of the …nal good is given by:
n 1
1
Yt = ! YH;t + (1
1
!) [(1
) YF;t ]
1
o
1
;
(26)
where ! denotes the fraction of home-produced goods that are used for the
production of the …nal good, and denotes the elasticity of substitution
between domestically produced and imported intermediate goods in both
37
= 0;
countries. The prices of these composite goods for the …nal good producers
are given by PH;t and PF;t .
The demand function for both types of goods is given by:
YH;t = !
PH;t
Pt
Yt ;
YF;t = (1
)(
!)(1
PF;t
Pt
1)
Yt ;
(27)
and the price level is given by:
h
Pt = ! (PH;t )1
+ (1
!) P F;t
i11
1
:
). That is, what matters for the
where we have de…ned P F;t = PF;t =(1
de…nition of the price level is the after-iceberg cost price of imported goods.
Finally, we can rewrite the weights as follows in the production function of
the …nal good:
h
1
1
1
Yt = ! YH;t + (1
where
(1
1
! ) (YF;t )
! ) = (1
!)(1
)
1
i
1
;
(28)
:
A higher rate of transportation costs , or an increase in the elasticity of
substitution decreases the value of (1 ! ), and raises the home bias in
the economy. In the Bayesian estimation of the model we …x the parameter
! and then estimate and .
A.2.2
Intermediate domestic composite goods producers
Intermediate domestic composite good producers buy di¤erentiated intermediate goods from domestic producers and aggregate them into the composite
domestic good. The composite intermediate domestic goods are:
YH;t =
1
n
"p
Z
n
YH;t (h)
"p 1
"p
"p
"p 1
dh
;
0
where "p > 1 denotes is the elasticity of substitution between types of
intermediate goods. The demand for each type of good is given by:
38
"p
PH;t (h)
YH;t (h) =
PH;t
and
1 "
PH;t p
A.2.3
1
=
n
YH;t ; for all h 2 [0; 1];
Z
n
1 "
PH;t p (h) dh:
(29)
(30)
0
Intermediate foreign composite goods producers
Intermediate foreign composite good producers export di¤erentiated intermediate goods from the foreign country by aggregating them into the composite
foreign good. The production function for composite …nal foreign goods is
given by
"p
"p Z 1
"p 1
"p 1
1
YF;t (f ) "p df
YF;t =
;
1 n
n
where "p > 1 denotes is the elasticity of substitution between types of intermediate goods. The demand for each type of good is given by:
YF;t (f ) =
"p
PF;t (f )
PF;t
YF;t ; for all f 2 [0; 1];
and
1 "
PF;t p
=
1
1
n
Z
1
1 "p
PF;t
(f ) df:
(31)
(32)
n
Once the intermediate composite goods are produced, a fraction is sold to
the domestic market and rest is sold to the other country through the …rms in
the transportation sector. Our baseline is a model with local currency pricing,
meaning that prices are sticky in the currency of the destination market and
the law of one price (without iceberg costs) does not hold outside the steady
state.
A.2.4
Intermediate Di¤erentiated Goods Producers
In each country, there is a continuum of intermediate goods producers, each
producing a type of good that is an imperfect substitute of the others, using
domestic capital and labor. These di¤erentiated intermediate goods are sold
to the composite di¤erentiated goods producers.
39
Technology The production function of each intermediate good in the
home country is given by
YH;t (h) + YH;t (h) = [At Nt (h) Xt ]1
[Kt
1
(h)] ;
(33)
where is the share of capital in the production function. The above production function has two technology shocks. The …rst one, Xt ; is a world
technology shock, that a¤ects the two countries the same way: it has a unit
root, as in Galí and Rabanal (2005), Lubik and Schorfheide (2006), and Rabanal and Tuesta (2010). In addition, there is a labor-augmenting country
speci…c technology shock, At ; that evolves as an AR(1) process. The evolution of technology shocks is as follows
log (Xt ) = log (Xt 1 ) + "xt ;
log(At ) = a log(At 1 ) + "at :
From cost minimization the real marginal cost of production is given by
M Ct (h) =
Wt =Pt
At
Xt1
1
(1
RtK
)(1
)
= M Ct :
Note that the marginal cost is not …rm-speci…c but rather depends on aggregate variables: all …rms receive the same technology shock and all …rms
rent inputs at the same price. The optimal capital-output ratio is also not
…rm-speci…c and given by:
Nt
(1
Nt (h)
=
=
Kt 1 (h)
Kt 1
)
RtK
Wt =Pt
:
(34)
Nominal Price Rigidities and Local Currency Pricing Once they
have solved for the optimal capital-output ratio and cost minimization, intermediate good producers choose the price that maximizes discounted pro…ts
subject to a Calvo-type restriction. In our baseline model, we assume local
currency pricing (LCP) for goods that are shipped internationally: a …rm
chooses a price for the domestic market and a price for the foreign market,
each price quoted in the destination market currency. Hence, there is price
stickiness in each country’s imports prices in terms of local currency.
In each period, a fraction 1
H of …rms that set prices in the domestic
market change their prices. Additionally, we assume that the prices of each
40
…rm that cannot reoptimize in a given period is adjusted according to the
indexation rules:
PH;t (h)
=(
PH;t 1 (h)
H;t 1 )
H
; and
PH;t (h)
=
PH;t 1 (h)
H
H;t 1
;
(35)
where 0 < H < 1: Therefore, conditioned on a having set an optimal
price from period t, the present discounted value of …rm h pro…ts is:
8 1
H
P
>
P (h) PH;t+k 1
>
( H )k t;t+k PH;t
M Ct+k YH;t+kjt (h)+
<
PH;t 1
t+k
k=0
M ax Et
1
H
P
St PH;t (h) PH;t+k 1
>
PH;t (h);PH;t (h)
>
M Ct+k YH;t+kjt (h)
( H )k t;t+k
:
Pt+k
P
H;t 1
k=0
(36)
where PH;t (h) and PH;t (h) are prices of good h in the home and foreign
markets, and whose evolution depends on the indexation rules, and YH;t+kjt (h)
and YH;t+kjt (h) are the associated demands for intermediate good h in each
country.
The …rst order conditions to the home intermediate goods producers …rms
for the home and foreign market are:
P^H;t (h)
"p
=
PH;t
"p 1
Et
1
P
(
k
H)
t;t+k M Ct+k YH;t+k
k=0
Et
1
P
k
(
H)
t;t+k YH;t+k
k=0
P^H;t (h)
"p
=
PH;t
"p 1
Et
Et
PH;t PH;t+k
PH;t+k Pt+k
1 "p
PH;t+k 1
PH;t 1
H
"p
H (1
PH;t+k 1
PH;t 1
>
>
;
"p )
;
(37)
1
P
k
H)
(
k=0
1
P
PH;t
PH;t+k
9
>
>
=
k=0
(
k
H)
M Ct+k
t;t+k RERt+k YH;t+k
t;t+k YH;t+k
PH;t
PH;t+k
PH;t PH;t+k
PH;t+k Pt+k
1 "p
PH;t+k 1
PH;t 1
PH;t+k 1
PH;t 1
H
"p
H (1
(38)
Equation (37) is the usual optimal price condition under a Calvo-type
restriction with indexation, and includes the demand coming from both domestic and foreign …rms. Equation (38) is the expression for the price of
exports and transforms the relevant real marginal cost of production to foreign currency by using the real exchange rate. Note that the coe¢ cients
re‡ecting the degree of nominal rigidity are the same for domestic in‡ation
and for exports.
41
"p )
:
;
The evolution of the home-produced intermediate goods price indices in
the home and foreign countries are, given indexation:
"
# 1 "p
H
1 "p
P
H;t 1
1 "
^
PH;t p = (1
+ H PH;t 1
;
(39)
H ) PH;t
PH;t 2
1 "p
PH;t
A.3
= (1
H)
P^H;t
1 "p
+
H
2
4PH;t
PH;t
PH;t
1
1
2
!
H
31
"p
5
:
(40)
Closing the Model
In order to close the model, we impose market-clearing conditions for all
types of home and foreign intermediate goods. For all aggregate intermediate goods, we need to take into account the size of the countries and transportation costs. Hence, we multiply per capita quantities by the size of each
sector.
nGDPt = n (At Nt Xt )1
Kt
1
= nYH;t + (1
n) YH;t + (1
n)(1
)YH;t :
Notice that a fraction of the exports is assigned to transportation costs
and the rest is demanded by the foreign country. For the …nal good, the
market clearing condition in the home country is:
(41)
Yt = Ct + It + Gt :
We introduce an exogenous demand shock for each country (Gt ; Gt ) which
can be interpreted as government expenditure shocks that evolve as AR(1)
processes in logs. We assume that both governments run a balanced budget
every period (i.e. Gt = Tt and Gt = Tt ).
The law of motion of the internationally traded bonds is written in aggregate terms and is given by :
nSt Dt
Pt R t
St Dt
Pt Yt
=
Ut
42
nSt Dt
1
+ N Xt
Pt
;
(42)
where real net exports ( NPXt t ) are given by
(1
N Xt
=
Pt
n)St PH;t YH;t
Pt
nPF;t YF;t
(43)
:
Finally, we assume that both countries follow a monetary policy rule that
targets deviations of domestic CPI in‡ation and real GDP growth from their
steady-state values, that we normalize to zero:
Rt
=
R
Rt 1
R
'R
[(Pt =Pt 1 )' (GDPt =GDPt 1 )'y ]
1 'R
exp("m
t ):
(44)
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46
47
Perceentage Points
Source: Haver Analytics.
-2.00
1999:Q1 2000:Q1 2001:Q1 2002:Q1 2003:Q1 2004:Q1 2005:Q1 2006:Q1 2007:Q1 2008:Q1 2009:Q1 2010:Q1 2011:Q1
-1.00
0.00
1.00
2 00
2.00
3.00
4.00
5.00
6.00
7.00
Figure 1
Monetary Policy Rates in United Kingdom and the Euro Area 1999 -2011
Difference
BoE
ECB
48
Exports plus Imporrts as Percentage of GDP
5.0
10.0
15.0
20.0
25.0
30.0
35.0
1992
1994
1996
1998
2000
Source: Direction of Trade Statistics, Haver Analytics.
1990
2002
2004
2006
2008
2010
Figure 2
Trade with Euro Area in France, Germany, Italy, Spain and the United Kingdom
1990 -2010
Germany
U.K.
Spain
Italy
France
49
Perceentage Points
-1.0
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
Source: Haver Analytics.
Figure 3
Risk Premium in France, Italy, Spain and the United Kingdom 1990 -2011
U.K.
Spain
Italy
France
A. GDP
B. Employment
Percentage Points
0.1
0.2
0
0
-0.1
-0.2
-0.2
-0.4
-0.3
-0.4
5
10
15
-0.6
20
-3
Percentage Points
C. Real Exchange Rate
0.6
15
0.4
10
0.2
5
0
0
-0.2
5
10
15
5
-5
20
Percentage Points
0.2
0.15
0
0.1
-0.2
0.05
10
15
20
5
10
15
20
F. Nominal Interest Rate
0.2
5
15
D. Net Exports / GDP
x 10
E. Inflation
0.4
-0.4
10
0
20
5
10
15
Quarters
Quarters
Independent Monetary Policy
Monetary Union
Figure 4: Impulse Response Functions to 1 percent increase in UIP Shock.
50
20
B. Welfare and Interest Rate Spread
0.5
1.5
0
Welfare
Welfare
A. Welfare and Iceberg Costs
2
1
0.5
0
-0.5
-0.5
-1
-1.5
0
-2
-100
2
4
6
8
Iceberg Costs
C. Welfare and Volatility of UIP Shocks
2
-50
0
50
100
150
200
Mean Interest Rate Spread
D. Welfare and Probability of a Financial Crisis
1
0
0
-2
-1
-4
-2
-6
Welfare
-8
0
0.2
0.4
0.6
0.8
1
Volatility of UIP Shocks
E. Welfare and Price Stickiness
-3
1.2
0
2
-1
0
-2
-2
-3
-4
-4
0
0.2
0.4
0.6
Calvo Parameter
-6
0.8
0
0.2
0.4
0.6
0.8
Probability of a Financial Crisis
F. Welfare and Wage Stickiness
0
0.2
0.4
0.6
Calvo Parameter
Welfare
Figure 5: Sensitivity Analysis of Welfare.
51
0.8
1